We review the problem of estimating parameters and unobserved trajectory components
from noisy time series measurements of continuous nonlinear dynamical systems. It is first …

This paper reviews the major developments of modeling techniques applied to nonlinear
dynamics and chaos. Model representations, parameter estimation techniques, data …

The paradigm of deterministic chaos has influenced thinking in many fields of science.
Chaotic systems show rich and surprising mathematical structures. In the applied sciences …

Inferring the laws of interaction in agent-based systems from observational data is a
fundamental challenge in a wide variety of disciplines. We propose a nonparametric …

Real life phenomena in engineering, natural, or medical sciences are often described by a
mathematical model with the goal to analyze numerically the behaviour of the system …

Considerable progress has been made in identifying the molecular composition of complex
signaling networks controlling cell proliferation, differentiation, and survival. However, to …

All self-respecting nonlinear scientists know self-organization when they see it: except when
we disagree. For this reason, if no other, it is important to put some mathematical spine into …

Motivation: Mathematical modelling of biological systems is becoming a standard approach
to investigate complex dynamic, non-linear interaction mechanisms in cellular processes …

We shed new light on the smoothness of optimization problems arising in prediction error
parameter estimation of linear and nonlinear systems. We show that for regions of the …

Reiterated measurements of an experimentally accessible quantity of a dynamical system
result in a time series, and one may wonder, what this information can tell about the system …